January 11, 2008

Regenerative Braking Energy

Regenerative braking is a significant part of the increased efficiency of hybrid vehicles. Out of curiosity, I did a few back-of-the-envelope calculations to figure out how much energy is involved with stopping different vehicles from different speeds.

The basic equation is 0.5mv^2 where m is the vehicle mass and v is velocity. Let’s take a look at a few different vehicles and the amount of energy that might be recouped during a stop. Most of the following calculations are done in metric units.

Assuming a 3,300 lb (1,500 kg – how convenient) sedan coming to a stop from 50 mph (22.4 m/s). That works out to 376 kilo Joules (kJ).

For a 44,000 lb (20,000 kg) vehicle such as a refuse truck making a stop from 20 mph (say 9 m/s) that’s 810 kJ.

Checking Wikipedia for the energy content of gasoline and diesel yields estimates of (32-34.8 MJ/L and 40.3 MJ/L respectively. As an aside, ethanol has estimated energy content of 18.4 to 21.2 MJ/L, seemingly barely half of that of diesel.

Another figure I’ve come across is from a NextEnergy brochure about hydraulic hybrid vehicles can “capture and reuse over 70% of the energy normally wasted during braking”. If you could do that for the above 3 scenarios, each of those stops would regenerate 263 kJ, 567 kJ, and 16,165 kJ respectively.

However, assuming gasoline engine efficiency of 25% and diesel engine efficiency of 35% (my SWAG) you would need 1,052 kJ (263 kJ / 0.25), 1,620 kJ (567 kJ/ 0.35), and 46,186 kJ respectively to generate that power from fuel. In other words, to get the tractor-trailer in this example moving from a stop to 65 mph takes about 1/3 gallon of diesel fuel.

All this energy is currently just wasted to the atmosphere as heat from regular disc or drum brakes to bring things to a stop. Depending on a vehicle’s typical drive cycle, there is substantial potential savings in regenerative braking. Which is why they’re starting to be used on heavy vehicles that do a lot of stop-and-go driving such as refuse trucks and delivery vans.

It comes down to balancing space requirements, added weight, cost, the volume and maximum pressure capability of the accumulator, and fuel savings. I wonder what applications they’ll appear on next.